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Cover: 9783540439325 | Limit Theorems for Stochastic Processes | Jean Jacod (u. a.) | Buch
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Limit Theorems for Stochastic Processes
Buch von Albert Shiryaev (u. a.)
Sprache: Englisch

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Beschreibung
Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an introduction to the theory of martingales and semimartingales, random measures stochastic integrales, Skorokhod topology, etc., as well asa large number of results which have never appeared in book form, and some entirely new results. The second edition contains some additions to the text and references. Some parts are completely rewritten.
Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an introduction to the theory of martingales and semimartingales, random measures stochastic integrales, Skorokhod topology, etc., as well asa large number of results which have never appeared in book form, and some entirely new results. The second edition contains some additions to the text and references. Some parts are completely rewritten.
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale Problems and Changes of Measures.- IV. Hellinger Processes, Absolute Continuity and Singularity of Measures.- V. Contiguity, Entire Separation, Convergence in Variation.- VI. Skorokhod Topology and Convergence of Processes.- VII. Convergence of Processes with Independent Increments.- VIII. Convergence to a Process with Independent Increments.- IX. Convergence to a Semimartingale.- X. Limit Theorems, Density Processes and Contiguity.- Bibliographical Comments.- References.- Index of Symbols.- Index of Terminology.- Index of Topics.- Index of Conditions for Limit Theorems.
Details
Erscheinungsjahr: 2002
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Grundlehren der mathematischen Wissenschaften
Inhalt: xx
664 S.
ISBN-13: 9783540439325
ISBN-10: 3540439323
Sprache: Englisch
Herstellernummer: 10886814
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Shiryaev, Albert
Jacod, Jean
Auflage: 2nd ed. 2003
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Grundlehren der mathematischen Wissenschaften
Maße: 241 x 160 x 43 mm
Von/Mit: Albert Shiryaev (u. a.)
Erscheinungsdatum: 10.10.2002
Gewicht: 1,185 kg
Artikel-ID: 103112883
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale Problems and Changes of Measures.- IV. Hellinger Processes, Absolute Continuity and Singularity of Measures.- V. Contiguity, Entire Separation, Convergence in Variation.- VI. Skorokhod Topology and Convergence of Processes.- VII. Convergence of Processes with Independent Increments.- VIII. Convergence to a Process with Independent Increments.- IX. Convergence to a Semimartingale.- X. Limit Theorems, Density Processes and Contiguity.- Bibliographical Comments.- References.- Index of Symbols.- Index of Terminology.- Index of Topics.- Index of Conditions for Limit Theorems.
Details
Erscheinungsjahr: 2002
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Grundlehren der mathematischen Wissenschaften
Inhalt: xx
664 S.
ISBN-13: 9783540439325
ISBN-10: 3540439323
Sprache: Englisch
Herstellernummer: 10886814
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Shiryaev, Albert
Jacod, Jean
Auflage: 2nd ed. 2003
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Grundlehren der mathematischen Wissenschaften
Maße: 241 x 160 x 43 mm
Von/Mit: Albert Shiryaev (u. a.)
Erscheinungsdatum: 10.10.2002
Gewicht: 1,185 kg
Artikel-ID: 103112883
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